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Abstract

Inverse lithography technology (ILT) treats photomask design for microlithography as an inverse mathematical problem. We show how the inverse lithography problem can be addressed as an obstacle reconstruction problem or an extended nonlinear image restoration problem, and then solved by a level set time-dependent model with finite difference schemes. We present explicit detailed formulation of the problem together with the first-order temporal and second-order spatial accurate discretization scheme. Experimental results show the superiority of the proposed level set-based ILT over the mainstream gradient methods.

Figures (3)

Fig. 1. Simulation of lithographic imaging with different mask patterns computed using different spatial schemes. The first column denotes the input U(x), the second column Iaerial(x), and the third column I(x). Row (a) uses the target circuit pattern I0 as input. Row (b) uses the pattern derived by our level set algorithm, with first-order temporal accuracy and ENO1 spatial accuracy. Row (c), (d) and (e) are similar to (b), but with ENO2, ENO3 and WENO spatial accuracy, respectively.

Fig. 2. Simulation of lithographic imaging with different mask patterns computed using different temporal schemes. The first column denotes the input U(x), the second column Iaerial(x), and the third column I(x). Row (a) uses the target circuit pattern I0 as input. Row (b) uses the pattern derived by our level set algorithm, with ENO2 spatial and first-order temporal accuracy. Row (c) and (d) are similar to (b), but with second-order and third-order temporal accuracy, respectively.

Table 3. Table 3. Normalized Computation Time (computation time in Fig. 3(b) and Fig. 3(d) using gradient method normalized against that in Fig. 3(c) and Fig. 1(c) using the proposed method, respectively) and Pattern Error (pixel difference) in Fig. 3

Normalized Computation Time (against that in Fig. 2(b) using first-order temporal accuracy) and Pattern Error (pixel difference) in Fig. 2

Table 3.

Table 3. Normalized Computation Time (computation time in Fig. 3(b) and Fig. 3(d) using gradient method normalized against that in Fig. 3(c) and Fig. 1(c) using the proposed method, respectively) and Pattern Error (pixel difference) in Fig. 3

Table 3.

Table 3. Normalized Computation Time (computation time in Fig. 3(b) and Fig. 3(d) using gradient method normalized against that in Fig. 3(c) and Fig. 1(c) using the proposed method, respectively) and Pattern Error (pixel difference) in Fig. 3